就 那条 发视频的 一视频 提到的结论 之 证明
即
m，n＞0
m²+n²=1
有
a/m^k+b/n^k
≥
(a^(2/(k+2))+b^(2/(k+2)))^((k+2)/2)
之
证明
有
m²+n²=1
即
-akm^(k-1)/m^(2k)
/
m
=
-bkn^(k-1)/n^(2k)
/
n
即
a/m^(k+2)
=
b/n^(k+2)
即
a/b=(m/n)^(k+2)
即
m=(a/b)^(1/(k+2))n
即
m
=
a^(1/(k+2))
/
(a^(2/(k+2))+b^(2/(k+2)))^(1/2)
n
=
b^(1/(k+2))
/
(a^(2/(k+2))+b^(2/(k+2)))^(1/2)
时
a/m^k+b/n^k
得
最小值
a(a^(2/(k+2))+b^(2/(k+2)))^(k/2)
/
a^(k/(k+2))
+
b(a^(2/(k+2))+b^(2/(k+2)))^(k/2)
/
b^(k/(k+2))
=
a^(2/(k+2))
(a^(2/(k+2))+b^(2/(k+2)))^(k/2)
+
b^(2/(k+2))
(a^(2/(k+2))+b^(2/(k+2)))^(k/2)
=
(a^(2/(k+2))+b^(2/(k+2)))
(a^(2/(k+2))+b^(2/(k+2)))^(k/2)
=
(a^(2/(k+2))+b^(2/(k+2)))^((k+2)/2)
即
m，n＞0
a/m^k+b/n^k
≥
(a^(2/(k+2))+b^(2/(k+2)))^((k+2)/2)
成立
得证
ps.
有关那条
是那什么
还想立牌坊
肮脏龌龊
腌臜不堪
“秒杀大招”
发视频的
无耻行径
详见
与
